36=-16t^2+40t+20

Solution for 36=-16t^2+40t+20 equation:

Simplifying
36 = -16t2 + 40t + 20

Reorder the terms:
36 = 20 + 40t + -16t2

Solving
36 = 20 + 40t + -16t2

Solving for variable 't'.

Combine like terms: 36 + -20 = 16
16 + -40t + 16t2 = 20 + 40t + -16t2 + -20 + -40t + 16t2

Reorder the terms:
16 + -40t + 16t2 = 20 + -20 + 40t + -40t + -16t2 + 16t2

Combine like terms: 20 + -20 = 0
16 + -40t + 16t2 = 0 + 40t + -40t + -16t2 + 16t2
16 + -40t + 16t2 = 40t + -40t + -16t2 + 16t2

Combine like terms: 40t + -40t = 0
16 + -40t + 16t2 = 0 + -16t2 + 16t2
16 + -40t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
16 + -40t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(2 + -5t + 2t2) = 0

Factor a trinomial.
8((1 + -2t)(2 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0.5, 2}